Abstract:
The main objective of this paper is to establish several new integral inequalities including k-Riemann–Liouville fractional integrals for convex, s-Godunova–Levin convex functions, quasi-convex, η-quasi-convex. In order to obtain our results, we have used classical inequalities as Hölder inequality, Power mean inequality and Weighted Hölder inequality. We also give some applications.
Keywords:η-quasi-convex, s-Godunova–Levin type, k-Riemann–Liouville fractional integral, Hölder inequality, weighted Hölder inequality, power mean inequality.
Citation:
S. I. Butt, B. Bayraktar, M. Umar, “Several new integral inequalities via k-Riemann–Liouville fractional integrals operators”, Probl. Anal. Issues Anal., 10(28):1 (2021), 3–22
\Bibitem{ButBayUma21}
\by S.~I.~Butt, B.~Bayraktar, M.~Umar
\paper Several new integral inequalities via $k$-Riemann--Liouville fractional integrals operators
\jour Probl. Anal. Issues Anal.
\yr 2021
\vol 10(28)
\issue 1
\pages 3--22
\mathnet{http://mi.mathnet.ru/pa313}
\crossref{https://doi.org/10.15393/j3.art.2021.8770}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000621661400001}
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https://www.mathnet.ru/eng/pa313
https://www.mathnet.ru/eng/pa/v28/i1/p3
This publication is cited in the following 4 articles:
B. Bayraktar, S. I. Butt, J. E. Nápoles, F. Rabossi, “Some new estimates of integral inequalities and their applications”, Ukr. Mat. Zhurn., 76:2 (2024), 159
B. Bayraktar, S. I. Butt, J. E. Nápoles, F. Rabossi, “Some New Estimates for Integral Inequalities and Their Applications”, Ukr Math J, 76:2 (2024), 169
B. Bayraktar, J. E. Nápoles, F. Rabossi, “On generalizations of integral inequalities”, Probl. anal. Issues Anal., 11(29):2 (2022), 3–23
B. Bairaktarov, Kh. E. Napoles Valdes, “Novye obobschennye integralnye neravenstva cherez (h,m)-vypuklye modifitsirovannye funktsii”, Izv. IMI UdGU, 60 (2022), 3–15
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